I’m DONE with Minus Signs

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  • Опубликовано: 19 дек 2024

Комментарии • 182

  • @WrathofMath
    @WrathofMath  День назад +21

    Let me know if you really wanna learn about multiplication and division in negative bases, I prepared notes on it but in the end I didn't think it was interesting enough to be worth the time.
    Join Wrath of Math to get exclusive videos, lecture notes, and more:
    ruclips.net/channel/UCyEKvaxi8mt9FMc62MHcliwjoin
    More math chats: ruclips.net/p/PLztBpqftvzxXQDmPmSOwXSU9vOHgty1RO

    • @veganwater381
      @veganwater381 16 часов назад

      I would love to! And also, is there a way to represent 0.99... in negadecimal? Does it involve imaginary numbers? Like 0.90..I + 0.09..?

    • @AstaryuuGaming
      @AstaryuuGaming 16 часов назад

      @@veganwater381 To convert the decimal component to negadecimal, every other place value starting with the tenths place increases the number to the left of it by 1 (if it is 9, it goes to 0 and subtracts 1 from the place to the left of that) and then is replaced by 10 minus itself. Therefore, 0.999... becomes... 1. Just 1.

    • @MichaelPiz
      @MichaelPiz 11 часов назад

      Your theme song for this video is obviously "Too Much Time on My Hands" by Styx.
      Also, you edited in the same audio snippet of the word "negadecimal" everywhere it appeared in the video, didn't you? That's effin' hilarious and proves that the song applies _hard._
      Also also, you introduced an _i_ at 20:38. That's just _mean!_
      Finally, you said early on that we can use _any_ number for a base. Oh yeah? Show me base _i,_ smart guy.
      😁
      P.S. I had commented two of the above quips separately in replies here but they disappeared. Let's see if this reply survives.

  • @dontuserachelslurs
    @dontuserachelslurs 20 часов назад +219

    Oh wow that's way easier than writing a small horizontal line

  • @Tostermz
    @Tostermz 17 часов назад +65

    “i realised there’s one big problem, and that is the country of canada and it’s ten provinces.”
    greatest maths video of all time

    • @MichaelPiz
      @MichaelPiz 11 часов назад +1

      Ah, Canada. That giant suburb of the Arctic Circle.

  • @error_6o6
    @error_6o6 16 часов назад +39

    if y’all (the viewers) think this is crazy wait till you find out about base 1+i. Yes, it is literally a complex-valued base.

    • @SimonClarkstone
      @SimonClarkstone 15 часов назад +8

      Or base Phi - looks like binary but there can be no adjacent 1s, and IIRC all integers are palindromes with the units place at the centre. If you don't like the inconvenient integers, you can approximate it using the Fibonacci numbers instead of powers of Phi.
      Even a matrix can be used as a base. All you need for your base is exponentiation (or similar function) by an integer, multiplication of that by an integer, then adding up load of those.

    • @ChessTopia
      @ChessTopia 12 часов назад

      Is not 1+i , it's 1×i

    • @wyattstevens8574
      @wyattstevens8574 12 часов назад

      Or -1+/-i? Combo Class reveals that this (that being either Gaussian integer with a magnitude of sqrt(2) and real part -1) is almost like "Gaussian binary!" ("Gaussian integers," in case you didn't know, is a name for numbers a+bi where a, b are in the ring Z)

  • @gary.h.turner
    @gary.h.turner 18 часов назад +82

    You used an awful lot of minus signs in your attempt to eliminate the use of the minus sign! 😂

    • @Salsmachev
      @Salsmachev 11 часов назад +3

      Yeah I feel like he didn't quiiite give it a fair shake. To do a negative carry in negadecimal addition, just add 19 instead of subtracting 1.

    • @merhaba3621
      @merhaba3621 11 часов назад +1

      You can also use a 10-adic number system

    • @WrathofMath
      @WrathofMath  10 часов назад +5

      still need to work on this plan 😂

    • @damianzieba5133
      @damianzieba5133 7 часов назад

      ​@@merhaba3621 and deal with x*y=0, x=/=0^y=/=0

  • @TonboIV
    @TonboIV 16 часов назад +21

    A truly wonderful solution! If only we could find a problem for it to solve!

  • @a_capitalist
    @a_capitalist 11 часов назад +13

    2:16 2:42 2:52 4:08 4:30 4:37 6:00 7:21 7:31 7:42 7:48 7:54 7:59 8:20 8:29 9:56 10:12 10:14 10:48 12:33 13:03 13:12 13:22 13:30 13:41 14:56 15:19 16:07 16:31 16:32 17:53 17:58 18:11 18:21 18:29 18:40 18:47 18:57 22:42 22:51 23:04 26:47 27:24 🤨📸

    • @WrathofMath
      @WrathofMath  11 часов назад +2

      😬

    • @regulus8518
      @regulus8518 8 часов назад +4

      it would have been way funnier if instead of using a stupid robot voice, you just asked a black friend to help you with this project 🤣🤣🤣

  • @txikitofandango
    @txikitofandango 20 часов назад +56

    1:45 nope it's 18 + 6 + 1 :)

    • @TheRandomPersonOnYoutube
      @TheRandomPersonOnYoutube 16 часов назад +1

      Yeah I kinda scratched my head on that one because I know 13 in base 10 is 111 in base 3. He probably just forgot to multiply the number to the power of the base

    • @BigFellaDj
      @BigFellaDj 14 часов назад

      thank god im not the only one who noticed

    • @2wr633
      @2wr633 13 часов назад

      @@TheRandomPersonOnRUclips i think what he forgot is the fact that he was talking about 221, as it seems like he just decided to add them up for no reason

    • @TheRandomPersonOnYoutube
      @TheRandomPersonOnYoutube 12 часов назад

      @@2wr633 I guess.

    • @TheRandomPersonOnYoutube
      @TheRandomPersonOnYoutube 11 часов назад

      ​@@2wr633I guess it can be true. Forgetting the numbers in their respective digits and just thinking about the sum of the exponents is a common mistake especially for me.

  • @Phyrior
    @Phyrior 12 часов назад +9

    Dude... I know April Fool's Day is amazing, but can you at least hold off until the actual day? I swear, they're making holidays closer and closer...

  • @JR13751
    @JR13751 19 часов назад +17

    Problem with negative bases is that carry is 2 digits.
    John Colson's Negativo-Affirmativo Arithmetik is better. It uses digits from -4 to +5.
    Edit: Carry can be one digit if it is negative.

    • @Hexa1296
      @Hexa1296 15 часов назад +1

      ah yeah, i usually call it signed decimal or balanced decimal

    • @thierrypauwels
      @thierrypauwels 10 часов назад +2

      Balanced numbers benefit from an odd base. 10 is not really a good base. With an odd base, rounding a number is merely removing the excess digits.

  • @LumberLopper
    @LumberLopper 19 часов назад +23

    Did RUclips not like using "nega-" as a prefix and it tried to interpret it as another word?

    • @KingGisInDaHouse
      @KingGisInDaHouse 19 часов назад +4

      what other word are you thinking of. Please say it so we all know exactly which word you are talking about.

    • @StylishHobo
      @StylishHobo 19 часов назад +12

      Nega, please.

    • @LumberLopper
      @LumberLopper 18 часов назад +1

      @@KingGisInDaHouse [redacted]

    • @gary.h.turner
      @gary.h.turner 18 часов назад +3

      Would nega-racism be hatred of your own race? 🤔

    • @AstaryuuGaming
      @AstaryuuGaming 17 часов назад +4

      Could be more than just a YT issue - for some American (meaning the American continent, not the USA) speakers, they literally sound the same

  • @J7Handle
    @J7Handle 19 часов назад +41

    Why are you unable to say the word negadecimal?

    • @StylishHobo
      @StylishHobo 19 часов назад +27

      What do you mean? He said it like 100 times. That's 100 times in *NEGADECIMAL*.

    • @ichimiustin8390
      @ichimiustin8390 18 часов назад +9

      He reused the audio for some reason

    • @davidmurphy563
      @davidmurphy563 18 часов назад +11

      I suspect he pronounced the first e and an i... Let's, um, not go there.

    • @AstaryuuGaming
      @AstaryuuGaming 17 часов назад +16

      The prefix "nega-" is pronounced the same as the N-word (no hard r) for some English speakers, and even for those that don't do that, the words are so similar sounding that it's better to be safe than sorry.

    • @eduardoxenofonte4004
      @eduardoxenofonte4004 17 часов назад +6

      @@AstaryuuGaming i'm pretty sure he was just doing it for the funny

  • @rzeqdw
    @rzeqdw 8 часов назад +2

    > There's one big problem, and that is the country of Canada
    I've been telling people that for years and nobody believes me!

  • @elunedssong8909
    @elunedssong8909 20 часов назад +5

    I thought about this idea before!
    My solution was have negative numbers every other number.
    so 100101 is 10^2 -10^1 + 10^0
    This makes us use twice the space to represent all numbers, though. Major downside, but addition still works the exact same. And multiplication / division you need to carry across 2 places instead of 1, which is a very simple/ intuitive change.

    • @Bengalnoestimido
      @Bengalnoestimido 17 часов назад +1

      Hmm if you take this idea but represent it in base 20, it would take up no more space than in decimal... i think?

    • @elunedssong8909
      @elunedssong8909 17 часов назад

      @@Bengalnoestimido Interesting idea, I can't figure out how to make it work.

  • @Hexa1296
    @Hexa1296 15 часов назад +2

    if you're worried about accidentally saying a slur, negative decimal also works

  • @RonuPlays
    @RonuPlays 15 часов назад +2

    Just as I was looking into bases with negative numbers this video pops up! Please do balanced number systems next (like balanced ternary), I find them fascinating!

    • @WrathofMath
      @WrathofMath  11 часов назад +2

      Perfect timing, I will!

  • @thierrypauwels
    @thierrypauwels 10 часов назад +1

    To remove the need of a minus sign to represent negative numbers, by far I prefer the balanced number systems. They still use a positive base, but have positive and negative digits, ideally the same number of positive and negative digits.

  • @IznbranahlGoose
    @IznbranahlGoose 9 часов назад

    When I first learned about it I really started enjoying playing with quaterimaginary which is 'base -2i' and lets you also fold the imaginary part of a complex number into a single 'base-4' series of numbers without negative signs or the awkward +(number)i part.
    When adding and subtracting you have the 'carries become borrows' flip flop and you have to skip over a digit since every other digit flip flops between real and imaginary.
    Remarkably multiplication works pretty much like regular multiplication except you have to deal with the oddities of 'carrying' and 'borrowing'. Division, on the other hand, is rather tricky but it has the one advantage of not having to compute a complex conjugate.

  • @nereisian
    @nereisian 13 часов назад +1

    Given the unfortunate pronounciation of negadecimal, I propose two alternatives:
    antidecimal: literally the opposite of decimal
    debtimal: debts can be viewed as having negative money

    • @WrathofMath
      @WrathofMath  11 часов назад

      I think antidecimal is good, though debtimal is pretty cute it only works well with decimal. Debternary isn't so smooth.

  • @coopergates9680
    @coopergates9680 19 часов назад +3

    Don't (b-1)s' complement and bs' complement (for base b) have advantages over negative bases? I'd rather write -(229) as 770 than having to use 190 just to represent ten.

  • @Roxor128
    @Roxor128 15 часов назад +2

    This makes me think of 2's complement, used for representing negative numbers in computers. The top-most place has a negative value, but the rest are positive.
    For example, for 8-bit numbers, the top bit has a value of -128, and the rest are +64 down to +1.

    • @TonyFisher-lo8hh
      @TonyFisher-lo8hh 13 часов назад

      Just stop being logical. Spoils a good fantasy story!

    • @WrathofMath
      @WrathofMath  11 часов назад

      cool, don't think I've ever heard of that

    • @n00bxl71
      @n00bxl71 9 часов назад

      Yes, but using the tens complement for negative numbers is far too logical. Negadecimal does not have this problem.

  • @themightyripples6582
    @themightyripples6582 18 часов назад +11

    I'm smoking weed and the "negadecimal" TTS was tripping me out but i did hear one time you forgot to switch the audio and said "decimal" rather than "negadecimal" - However you're presenting this very well and unless you weren't paying attention to what was happening you would know what you meant anyways... so rather than time stamping it I simply kept watching until hearing the TTS so much drove me to point this out. lmao!
    Great videos tho, I watch a lot of math creators here and you somehow stand out a lot of the time and also the videos have good quality!

    • @erikrichards6944
      @erikrichards6944 17 часов назад

      I too came here high wondering what the hell was up that. 😂

  • @DougTheDouglyDragon
    @DougTheDouglyDragon 20 часов назад +5

    I LOVE BASES ❤

    • @StylishHobo
      @StylishHobo 19 часов назад +1

      BASED

    • @MichaelPiz
      @MichaelPiz 10 часов назад

      This video makes it to (negative) 10th base.

  • @jan-pi-ala-suli
    @jan-pi-ala-suli 12 часов назад +1

    go all in and use a complex base like -1+i

  • @AstaryuuGaming
    @AstaryuuGaming 17 часов назад

    Fun fact: -1 in base 10 is 19 in base -10, so in the example of 34 + 89 in base -10, you can also think of that -1 carry into the hundreds place as sticking -1 in negadecimal to the front.

  • @hazevthewolf178
    @hazevthewolf178 20 часов назад +1

    You've no way of knowing this upfront, but this video came along at just the right time. As one of my favourite fictional people would say, "Decidedly, I am unwell." This is a fun topic and I enjoyed your easy to follow exposition of it. When I go back to bed, in the spirit of one of Lewis Carroll's pillow problems, I'm going to bring a notepad and pencil with me and play with this concept. Cheers!

  • @sirnicholasiii
    @sirnicholasiii 19 часов назад +14

    every base is base 10

    • @paperwhite3853
      @paperwhite3853 18 часов назад +3

      Base 2 and base -i×sqrt(e^2) are shocked by this basephobic comment

    • @Why553-k5b_1
      @Why553-k5b_1 18 часов назад

      proof?

    • @leeprice133
      @leeprice133 17 часов назад

      ​​​@@Why553-k5b_1the base number is always written as '10' in any positional numeral system using Arabic numerals. The word 'ten' and the numeral '10' only represent the same thing in decimal.

    • @rubenvanderark4960
      @rubenvanderark4960 15 часов назад +4

      ​@@Why553-k5b_1in base 2, 2 is written as 10. Therefore in base 2, you can say "this is base 10".
      This works for any number because n^1=n, so every base will be represented by one copy of the base to the power of one (a 1 in what we call the "tens digit" in base ten) and zero copies of the base to the power of zero (a 0 in the ones digit), or 10

    • @avovk1852
      @avovk1852 13 часов назад

      which is base 1010 itself

  • @AlreschaAndromeda
    @AlreschaAndromeda 18 часов назад

    Unless you modified the alternating sign for even terms only, so that negadecimal are symmetrical to the posidescimal
    I.e.: -1 (base 10) = 1 (base -10)

  • @FaerieDragonZook
    @FaerieDragonZook 14 часов назад +2

    Balanced Ternary is a fun and overpowered system.

    • @WrathofMath
      @WrathofMath  11 часов назад +1

      Definitely got that one on my list, it's very cute and I didn't want to bring it up here because it's too fun to just mention and not dig into

    • @thierrypauwels
      @thierrypauwels 10 часов назад

      Balanced ternary is my favourite. Rounding a number is nothing else than cutting the excess decimals. You can start an addition of many numbers without knowing whether the result will be positive or negative. Ideal to represent quantities that have no natural zero point. In particular every scale that is logarithmic. A drawback is that one half has no finite representation, but two infinite sequences of digits: zero, decimal point, followed by infinitely many 1s, or one, decimal point, followed by infinitely many (-1)s.

    • @FaerieDragonZook
      @FaerieDragonZook 10 часов назад +1

      Some benefits of Balanced Ternary:
      Extremely good radix economy
      No - sign needed.
      Only 2/9 carries in addition table, even better than the 1/4 of binary.
      Negation is just flipping all the (+1) symbols to (-1) and vice versa.

  • @gcewing
    @gcewing 15 часов назад +2

    So Canada has 10 provinces... or is that -10 provinces... I'm so confused.

    • @MichaelPiz
      @MichaelPiz 10 часов назад

      There's nothing positive about Canada, especially the temperatures.

  • @nanettepaschall3006
    @nanettepaschall3006 9 часов назад +1

    why couldnt it be called inverdecimal

  • @thegrandminority8890
    @thegrandminority8890 11 часов назад

    "No matter what base we use..." Twos compliment be like

  • @shgysk8zer0
    @shgysk8zer0 19 часов назад +1

    What about signed bases? As-in signed binary representing {-1, 0, 1} and being notated by {0, 1, 2} (0-index). Or something like that.

    • @tylerduncan5908
      @tylerduncan5908 15 часов назад +1

      This is called a balanced system. Balanced ternary is somewhat common in a couple fields dealing with electronics.

  • @AlkalineOrSomething
    @AlkalineOrSomething 19 часов назад +3

    0:43 uncalled for

  • @ricardojuliao84
    @ricardojuliao84 7 часов назад

    Ok,now you have to redefine all the Math

  • @MGSchmahl
    @MGSchmahl 14 часов назад +1

    Now do quaterimaginary

    • @WrathofMath
      @WrathofMath  11 часов назад +1

      it's on my todo list; right after using a Clue board to do the integral calculus

  • @2wr633
    @2wr633 12 часов назад +1

    should have wrote the carry as 19 :)

  • @whtiequillBj
    @whtiequillBj 14 часов назад

    why would you need subtraction or division with negadecimal? Isn't it redundant to the system its self? Also inversion is redundant.

  • @Golden_Official100
    @Golden_Official100 10 часов назад

    I love [[negadecimal]], and I understand why you'd use a TTS

  • @wyattstevens8574
    @wyattstevens8574 12 часов назад

    My eyes: *see the thumbnail*
    My brain: * "Hello folks, and welcome back to Combo Claaa-" * (let me know if you caught that reference!)

    • @WrathofMath
      @WrathofMath  11 часов назад

      his sets are very whimsical, I'd like to hang out with the guy

    • @wyattstevens8574
      @wyattstevens8574 11 часов назад

      @@WrathofMath I thought about that because he talked negative bases once! And the "trail-off" (ellipses) was supposed to symbolize a crashing clock!

  • @kornsuwin
    @kornsuwin 20 часов назад

    the intro is a strong start

    • @WrathofMath
      @WrathofMath  10 часов назад

      let not the terrors reach you

  • @timstorer978
    @timstorer978 6 часов назад

    Who is that guy in the crowd that keeps shouting "in negadecimal?"

  • @davidnoll9581
    @davidnoll9581 12 часов назад

    I was thinking about a similar thing with an imaginary base. I guess you would need 2 of them... and I guess the numbers couldn't quite be the same base... one would still be multiplied by i, so not that cool after all, just basically changing the base of the coefficients of the normal complex plane... but still interesting to think the complex plane as a pair of coordinates in a negadecimal coordinate system. Guess it would be sort of like splicing the top and bottom halves of the plane? Wonder what the riemann zeta funciton would look like represented that way..

  • @xavariusquest4603
    @xavariusquest4603 12 часов назад

    I'm intrigued by 3 ÷ 10 being 1 remainder 7.
    Oh....and you cannot restore the original value because the introduction of subtraction allows a group of possible solutions but not ONE solution.
    This was silly

  • @rainerzufall42
    @rainerzufall42 7 часов назад

    8:24 Wrong use of carry!!!

  • @orangesite7625
    @orangesite7625 15 часов назад

    The thumbnail 😂😂😂

  • @mauriceprosper9730
    @mauriceprosper9730 16 часов назад

    I lost it with the TTS at 9:08

  • @Cynderace
    @Cynderace 9 часов назад

    bro says [[ Negadecimal ]] like he’s spamton g spamton

  • @matthijshebly
    @matthijshebly 16 часов назад +2

    Check out Balanced Ternary

  • @jaydentplays7485
    @jaydentplays7485 14 часов назад

    Oh am I a problem now? After all those unsolved equations? 9-15. 6-12. 44-121

  • @torfley
    @torfley 18 часов назад +2

    negawatt?

  • @brenatevi
    @brenatevi 11 часов назад

    I found the "negadecimal" voice in hilarious.

    • @WrathofMath
      @WrathofMath  11 часов назад

      I ain't getting caught on any slips!

  • @alicesproul8155
    @alicesproul8155 17 часов назад

    how does one count in negadecimal?

    • @WrathofMath
      @WrathofMath  10 часов назад

      1, 2, 3, 4, 5, 6, 7, 8, 9, 190, ...

  • @oenwilson2486
    @oenwilson2486 19 часов назад +4

    okay but why is every mention of "negadecimal" just the same audio copy pasted throughout the video and adds an unnecessary emphasis to its name... it bothers me a lot and it sounds more like he's *really* hammering on what the prefix of the number system is...

    • @StylishHobo
      @StylishHobo 19 часов назад +3

      It's a joke

    • @swirlingvortex09
      @swirlingvortex09 18 часов назад +7

      Wrath of Math HAS to do this.
      If he speaks "negadecimal" normally and there isn't enough spoken emphasis on the "e"... it would sound like a slur and be treated as a slur.
      It is way less socially messy for the Microsoft TTS or phonetic sound file to be there.

  • @ThePsyko420
    @ThePsyko420 9 часов назад

    It seems to me -94 is more concise than 1906

  • @TeagueChrystie
    @TeagueChrystie 9 часов назад

    yeah this is much simpler than "minus"

  • @SixtyStone
    @SixtyStone 13 часов назад

    Ah yes using 2 bases and introducing confusion instead of writing one simple line

  • @proboiz_50
    @proboiz_50 16 часов назад

    There are 7251 views right now in _nega decimal_ base

  • @SixtyStone
    @SixtyStone 13 часов назад

    Ah yes Canada invented negative numbers.

    • @WrathofMath
      @WrathofMath  11 часов назад

      they're a wily bunch

    • @SixtyStone
      @SixtyStone 9 часов назад

      @WrathofMath I'm ao glad they gave this away to us otherwise math would be uhh less uhm insert word here

  • @naoromi9883
    @naoromi9883 18 часов назад

    Negadecimal can i borrow a fry

  • @ernesto.iglesias
    @ernesto.iglesias 12 часов назад

    I think he will left the giant elephant in the room for the end. How do you represent the positive 10, 1000, 0.1 or any 10^(2n+1)? 😅

    • @WrathofMath
      @WrathofMath  11 часов назад

      Easy! For 10 in base -10, just think of it as adding 100 and taking away 90, so it is 190. For 1000 it's like adding 10000 and taking away 9000, so 19000.

    • @shaggygoat
      @shaggygoat 11 часов назад

      10₁₀, 1000₁₀, 0.1₁₀ and 10^(2n+1) may be represented as 190, 19000, 1.9 and 10^(2n+2) + 9×10(2n+1), respectively.

  • @oneoftheHongKongers
    @oneoftheHongKongers 10 часов назад

    2:16

  • @fredrik3685
    @fredrik3685 17 часов назад

    I don't want to sound negative but.....

  • @elliotsyptyst
    @elliotsyptyst 16 часов назад +1

    a WHAT decimal

  • @misterlau5246
    @misterlau5246 8 часов назад

    Aw, dude 😅🤓😈
    I'll keep using linear algebra to represent negatives in an affine space of the positives 🤓🤣

  • @sebas31415
    @sebas31415 13 часов назад +1

    I can't say that I'm white

  • @mistersir3020
    @mistersir3020 8 часов назад

    Lol we can't do math because of N.

  • @epicstar86
    @epicstar86 8 часов назад

    aight man

  • @ammhg8642
    @ammhg8642 12 часов назад +2

    👍

    • @WrathofMath
      @WrathofMath  11 часов назад +1

      don't be so negative

    • @henrycook859
      @henrycook859 10 часов назад

      ​@@WrathofMathits a popular internet meme to put nega as a prefix before a unit. Be honest, did you intentionally clickbait the title?

    • @WrathofMath
      @WrathofMath  10 часов назад

      not sure what you mean, I'm not genuinely done using minus signs and converting my whole life to 🤖N E G A D E C I M A L🤖 if that's your question

    • @ammhg8642
      @ammhg8642 10 часов назад

      @@WrathofMath guess it was a misunderstanding
      I thought you were like VSauce, with a funny thumbnail and content
      Its just maths i didn't know

  • @UK_parliament_English
    @UK_parliament_English 19 часов назад +1

    I like the system! But i think I’ll (sadly) have to stick to the “meddling” (-) symbol.

    • @WrathofMath
      @WrathofMath  10 часов назад

      Unfortunately that meddling symbol does have its conveniences

  • @GameJam230
    @GameJam230 18 часов назад

    Tbh I’ve always thought the concept of inverse functions (subtraction) to be such an odd concept, as they almost always introduce the requirement for new types of numbers to exist.
    Allowing an inverse of addition allows the possibility that there may exist a number such that 5 + X = 2, which without negatives is not possible.
    Division as an inverse establishes the possibility that there exists a number such that 6 * X = 2, which isn’t possible without fractional numbers. It also allows some additional solutions to older equations, like being able to identify -2 and -7 as valid divisors (if even atypical) for the number 14
    The creation of exponentiation actually establishes multiple new types of number depending on the context “inverse” is used in.
    One occurs by placing fractional values in the exponent, which is what we know as roots. These create two new types of number, through irrationals like the square root of 2, but also it establishes the need for a solution to the equation X^2 = -1, which establishes the imaginary numbers, or complex numbers which can also be added component-wise with “real” numbers.
    The other type of inverse to exponentiation occurs as the solution to equations like 18^X = 5, in which case we need logarithms.
    What I wonder is whether or not any other useful new types of numbers can be decided in this same way; by creating a function, defining its inverse, and then solving an equation that produces a result outside the domain of the original function.
    I mean, you can define new rules all you want, really, like saying there’s zero-divisors, or the Eisenstein integer system, or suggesting that there is a result when dividing by 0, and so on. New number systems can be made just fine, but what I’m more curious about is if our EXISTING number system can be expanded naturally this way, such as by defining an inverse to tetration.

  • @blue_alan.becker__real
    @blue_alan.becker__real 11 часов назад

    9h ago

  • @Xeroisawesome
    @Xeroisawesome 16 часов назад +1

    So however this video got recommended to me, I strongly regret it. You successfully managed to waste around fove minutes of my life. Perhaps the worst part of all this is your bizarre insistence on having some AI voice say "negadecimal" in a jarring tone shift each time. Have fun with your overcomplicated BS and irrational fear of the prefix "nega"

  • @atimholt
    @atimholt 19 часов назад

    I was hoping the solution would be to subtract the magnitude of the negative number from an infinite string of nines going off to the left.

    • @WrathofMath
      @WrathofMath  10 часов назад

      a fun activity for another time, no doubt!

  • @KingGisInDaHouse
    @KingGisInDaHouse 19 часов назад

    I dont like it. How do we know how far -7 is from -20 is geometrically from this.

  • @AlreschaAndromeda
    @AlreschaAndromeda 18 часов назад

    Negadecimal is sucks! Because minus ten to the power of even number is always positive

    • @WrathofMath
      @WrathofMath  10 часов назад

      What's wrong with -10 to even powers always being positive? I think it's charming!

  • @itzmetanjim
    @itzmetanjim 19 часов назад

    change the name to MEGAdecimal. unintuitive but MUCH MUCH cooler.

  • @TheObstalace
    @TheObstalace 15 часов назад +1

    N E G A D E C I M A L